Filtering Time Series with Penalized Splines Göran Kauermann∗

The decomposition and filtering of time series is an important issue in economics and econometrics and related fields. Even though there are numerous competing methods on the market, in applications one often meets one of the few favorites, like the Hodrick & Prescott filter or the Bandpass filter. In this paper we suggest to employ penalized splines fitting for detrending, extending recent results of Krivobokova & Kauermann (2007). The approach allows to take correlation of the residuals into account and provides a data driven setting of the smoothing parameter, none of which the classical filters allow. We show the simplicity of the penalized spline filter using the open source software R and demonstrate differences and features with numerous data examples taken from Stock & Watson (1999)